Dear Drs. Muthen: I am trying to test a cross-level interaction model with a level-2 moderator. Specifically, I have a group level (level -2) IV, an individual level (level-1) DV, and a group level (level-2) moderator. This is consistent with traditional HLM model with a high-level moderator. I read related threads in the M-plus discussion. However I am not sure if my codes are correct since the estimation results are very different from my estimation in HLM. It would be great if you could check if my M-Plus codes are correct. Thank you! Sincerely, Jae

See Example 9.2 which shows a cross-level interaction. The random slope should be defined on the within level. You will obtain the same results in Mplus and HLM if you have the same model, data, and estimator.

However I don't think we are on the same page. Example 9-2 is not what I am trying to do. In my model, IV is a level-2(group) observed variable. Thus, this can not be modeled as a random slope on the within level. In my data, everybody in the same group has the same value for the IV.

In example 9-2, x is a within level observed variable. This means that observations in the same group would have different values for the IV.

Also, I am modeling an interaction term between my between level IV and another between level covariate.

Would you please check my Mplus code based on my further explanations? Thank you so much!

Yes, it looks like you are using XWITH correctly. I wouldn't call your model a cross-level interaction since the between-level covariate doesn't multiply a within-level covariate. Cross-level interactions happen when you have a random slope on Within. Also, I don't see how it can be compared to regular HLM since regular HLM doesn't work with general latent variable models.

Thank you for checking my codes, Dr. Muthen. If my codes are correct, then I think I should play with my data for a while. Considering that reliabilities of the measures I used in HLM is quite high, the discrepancy I found between HLM and Mplus results are quite surprising.

If you specify the same model and use the same data and estimator, the Mplus results will agree with HLM. Please send the Mplus and HLM outputs and your license number to support@statmodel.com and we will show you your error.